{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:GQQN3OXGMRPNV5TWGHPWVHAAT2","short_pith_number":"pith:GQQN3OXG","canonical_record":{"source":{"id":"1410.1653","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-10-07T09:44:06Z","cross_cats_sorted":["cs.CC","math.CO"],"title_canon_sha256":"510b6a441367fb3e6cf1382caabf56fbadc8b7faddead911e21cedaa774c04a3","abstract_canon_sha256":"efe7005e1ad55e857143731d305489677d55682d683a3cd87bdd94f4c21e74f3"},"schema_version":"1.0"},"canonical_sha256":"3420ddbae6645edaf67631df6a9c009e98edb03c3cbe9dc1c141d3b9423eefe4","source":{"kind":"arxiv","id":"1410.1653","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.1653","created_at":"2026-05-18T02:40:55Z"},{"alias_kind":"arxiv_version","alias_value":"1410.1653v1","created_at":"2026-05-18T02:40:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.1653","created_at":"2026-05-18T02:40:55Z"},{"alias_kind":"pith_short_12","alias_value":"GQQN3OXGMRPN","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GQQN3OXGMRPNV5TW","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GQQN3OXG","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:GQQN3OXGMRPNV5TWGHPWVHAAT2","target":"record","payload":{"canonical_record":{"source":{"id":"1410.1653","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-10-07T09:44:06Z","cross_cats_sorted":["cs.CC","math.CO"],"title_canon_sha256":"510b6a441367fb3e6cf1382caabf56fbadc8b7faddead911e21cedaa774c04a3","abstract_canon_sha256":"efe7005e1ad55e857143731d305489677d55682d683a3cd87bdd94f4c21e74f3"},"schema_version":"1.0"},"canonical_sha256":"3420ddbae6645edaf67631df6a9c009e98edb03c3cbe9dc1c141d3b9423eefe4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:55.158455Z","signature_b64":"OZmJDXR1no912NxzJd/Zej474Op1Uh9bDFMqH9lmXj4f0Jd6+RRC5pnDinE5w+6p9y5VBaJlXQ8XlFzYILrXAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3420ddbae6645edaf67631df6a9c009e98edb03c3cbe9dc1c141d3b9423eefe4","last_reissued_at":"2026-05-18T02:40:55.157873Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:55.157873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.1653","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:40:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xaL+pdQJXY4Aw0UNJwh32fMCuUKgJjDGyCCMECJ9sluOzko8gQzAzCjnEvu8pMRpTYFPtrLuYX7rM5tFjSdfAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:13:14.999708Z"},"content_sha256":"3b598f83976f1f94ad22e44ea3300b4277872d02983ab308dfd7fc7827ba7f7f","schema_version":"1.0","event_id":"sha256:3b598f83976f1f94ad22e44ea3300b4277872d02983ab308dfd7fc7827ba7f7f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:GQQN3OXGMRPNV5TWGHPWVHAAT2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Notes on dual-critical graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.CO"],"primary_cat":"cs.DS","authors_text":"S\\'andor Kisfaludi-Bak, Zolt\\'an Kir\\'aly","submitted_at":"2014-10-07T09:44:06Z","abstract_excerpt":"We define dual-critical graphs as graphs having an acyclic orientation, where the indegrees are odd except for the unique source. We have very limited knowledge about the complexity of dual-criticality testing. By the definition the problem is in NP, and a result of Bal\\'azs and Christian Szegedy provides a randomized polynomial algorithm, which relies on formal matrix rank computing. It is unknown whether dual-criticality test can be done in deterministic polynomial time. Moreover, the question of being in co-NP is also open.\n  We give equivalent descriptions for dual-critical graphs in the g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1653","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:40:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jLxCeESMtUvHfzF4RUowOTI7bccuTGOslysF5e/s3Lr/CJzWtaY2a6vOQN1rg09SXPcHPnFNAk0n1YlmbeGSBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:13:15.000399Z"},"content_sha256":"497cd332da8f7efc4a8dc0cb5e501c9afa2420cb7901689a67d4c39f32896de6","schema_version":"1.0","event_id":"sha256:497cd332da8f7efc4a8dc0cb5e501c9afa2420cb7901689a67d4c39f32896de6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GQQN3OXGMRPNV5TWGHPWVHAAT2/bundle.json","state_url":"https://pith.science/pith/GQQN3OXGMRPNV5TWGHPWVHAAT2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GQQN3OXGMRPNV5TWGHPWVHAAT2/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-12T00:13:15Z","links":{"resolver":"https://pith.science/pith/GQQN3OXGMRPNV5TWGHPWVHAAT2","bundle":"https://pith.science/pith/GQQN3OXGMRPNV5TWGHPWVHAAT2/bundle.json","state":"https://pith.science/pith/GQQN3OXGMRPNV5TWGHPWVHAAT2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GQQN3OXGMRPNV5TWGHPWVHAAT2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GQQN3OXGMRPNV5TWGHPWVHAAT2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"efe7005e1ad55e857143731d305489677d55682d683a3cd87bdd94f4c21e74f3","cross_cats_sorted":["cs.CC","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-10-07T09:44:06Z","title_canon_sha256":"510b6a441367fb3e6cf1382caabf56fbadc8b7faddead911e21cedaa774c04a3"},"schema_version":"1.0","source":{"id":"1410.1653","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.1653","created_at":"2026-05-18T02:40:55Z"},{"alias_kind":"arxiv_version","alias_value":"1410.1653v1","created_at":"2026-05-18T02:40:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.1653","created_at":"2026-05-18T02:40:55Z"},{"alias_kind":"pith_short_12","alias_value":"GQQN3OXGMRPN","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GQQN3OXGMRPNV5TW","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GQQN3OXG","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:497cd332da8f7efc4a8dc0cb5e501c9afa2420cb7901689a67d4c39f32896de6","target":"graph","created_at":"2026-05-18T02:40:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We define dual-critical graphs as graphs having an acyclic orientation, where the indegrees are odd except for the unique source. We have very limited knowledge about the complexity of dual-criticality testing. By the definition the problem is in NP, and a result of Bal\\'azs and Christian Szegedy provides a randomized polynomial algorithm, which relies on formal matrix rank computing. It is unknown whether dual-criticality test can be done in deterministic polynomial time. Moreover, the question of being in co-NP is also open.\n  We give equivalent descriptions for dual-critical graphs in the g","authors_text":"S\\'andor Kisfaludi-Bak, Zolt\\'an Kir\\'aly","cross_cats":["cs.CC","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-10-07T09:44:06Z","title":"Notes on dual-critical graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1653","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3b598f83976f1f94ad22e44ea3300b4277872d02983ab308dfd7fc7827ba7f7f","target":"record","created_at":"2026-05-18T02:40:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"efe7005e1ad55e857143731d305489677d55682d683a3cd87bdd94f4c21e74f3","cross_cats_sorted":["cs.CC","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-10-07T09:44:06Z","title_canon_sha256":"510b6a441367fb3e6cf1382caabf56fbadc8b7faddead911e21cedaa774c04a3"},"schema_version":"1.0","source":{"id":"1410.1653","kind":"arxiv","version":1}},"canonical_sha256":"3420ddbae6645edaf67631df6a9c009e98edb03c3cbe9dc1c141d3b9423eefe4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3420ddbae6645edaf67631df6a9c009e98edb03c3cbe9dc1c141d3b9423eefe4","first_computed_at":"2026-05-18T02:40:55.157873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:55.157873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OZmJDXR1no912NxzJd/Zej474Op1Uh9bDFMqH9lmXj4f0Jd6+RRC5pnDinE5w+6p9y5VBaJlXQ8XlFzYILrXAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:55.158455Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.1653","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b598f83976f1f94ad22e44ea3300b4277872d02983ab308dfd7fc7827ba7f7f","sha256:497cd332da8f7efc4a8dc0cb5e501c9afa2420cb7901689a67d4c39f32896de6"],"state_sha256":"27afc37c417937c080ecca66e58acad838a25fdfecf4e6dca295aece4478c30f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gyT925Kwws2z9uLh6mHX5XjYUDjQI0pFUV3uPeRSLCKidtrH9ucxmLuTzV7fW7yNz0AqWhn+xTKtap7XChvQDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T00:13:15.004095Z","bundle_sha256":"7755d6a552901f2b87708893abadd5ea376b4bbac5457ff91aa7fbaf6ea85891"}}